12 is kind of young to be doing this but it's fairly common for older teenagers. I'd try completely (and I mean completely) ignoring it/her for a week and see it gives her time to actually think about what's she's doing, and maybe come clean if there is something wrong at school. Cook her meals and all the normal stuff just don't engage in much conversation, giving the cold shoulder where possible.
Sometimes an issue like this can become so entrenched that people just dig their heels in and loose sight of why they're actually behaving the way they are. Teenagers can be very stubborn, and I feel the shock of being ignored could bring her round. No one like’s to be marginalise, and she’ll eventually start to feel lonely and will want someone to confide in.